Parametric study of the nonisothermal <Emphasis Type="Italic">n</Emphasis><Superscript>th</Superscript>-order distributed activation energy model involved the Weibull distribution for biomass pyrolysis

This paper describes the influences of some parameters relevant to biomass pyrolysis on the numerical solutions of the nonisothermal n ^th-order distributed activation energy model (DAEM) involved the Weibull distribution. Investigated parameters are the integral upper limit, the frequency factor, heating rate, the reaction order and the shape, scale and location parameters of the Weibull distribution. Those influences can be used for the determination of the kinetic parameters of the nonisothermal n ^th-order Weibull DAEM from thermoanalytical data of biomass pyrolysis.     

Improved version of Doyle integral method for nonisothermal kinetics of solid-state reactions

An improved version of Doyle integral method for the determination of the kinetic parameters from nonisothermal thermoanalytical data has been presented. The relative errors involved in the activation energy and frequency factor determined from Doyle integral method and its improved integral method have been estimated. The results have shown that the precision of the improved version of Doyle integral method for the determination the kinetic parameters (including the activation energy and frequency factor) is much higher than that of Doyle integral method.     

Kinetics of the exothermic decomposition of 1-nitro-3-(β,β,β-trinitroethyl)-4,5-dinitroiminoimidazolidine-2-one

The kinetic parameters of the exothermic decomposition of the title compound in a temperatureprogrammed mode have been studied by means of DSC. The DSC data obtained are fitted to the integral, differential, and exothermic rate equations by the linear least-squares, iterative, combined dichotomous, and least-squares methods, respectively. After establishing the most probable general expression of differential and integral mechanism functions by the logical choice method, the corresponding values of the apparent activation energy (E _a), preexponential factor (A), and reaction order (n) are obtained by the exothermic rate equation. The results show that the empirical kinetic model function in differential form and the values of E _a and A of this reaction are (1 − α)^−4.08, 149.95 kJ mol⁻¹, and 10^14.06 s⁻¹, respectively. With the help of the heating rate and kinetic parameters obtained, the kinetic equation of the exothermic decomposition of the title compound is proposed. The critical temperature of thermal explosion of the compound is 155.71°C. The above-mentioned kinetic parameters are quite useful for analyzing and evaluating the stability and thermal explosion rule of the title compound. The text was submitted by the authors in English.     

Kinetic analysis of solid-state reactions: A new integral method for nonisothermal kinetics with the dependence of the preexponential factor on the temperature (A = A0Tn)

In this study, we have proposed a new approximation for the general temperature integral, which frequently occurs in the nonisothermal kinetics with the dependence of the preexponential factor on the temperature and has no exact analytical solution. The validity of the new approximation has been tested by some numerical analyses. As the solution of the general temperature integral, the new approximation is more accurate than other approximations. Based on the newly proposed approximation, the corresponding integral method has been given. The precision of the integral methods for the determination of the activation energy has been calculated, and the results have shown that the relative error involved in the activation energy obtained from the new integral method is smaller than that from other integral methods. For applications, nonisothermal data obtained by theoretical simulation have been successfully processed using the new integral method.     

Errors involved in the activation energy calculated by integral methods when the frequency factor depends on the temperature ( A = A 0 T m)

The dependence of the frequency factor on the temperature (A=A ₀ T ^m) has been examined and the errors involved in the activation energy calculated from some integral methods without considering such dependence have been estimated. Investigated integral methods are the Coats-Redfern method, the Gorbachev-Lee-Beck method, the Wanjun-Yuwen method and the Junmeng-Fusheng method. The results have shown that the error in the determination of the activation energy calculated ignoring the dependence of the frequency factor on the temperature can be rather large and it is dependent on x=E/RT and the exponent m.     

New approximation for the general temperature integral

A new approximation has been proposed for calculation of the general temperature integral $ \int\limits_0^T {T^m } e^{ - E/RT} dT $ \int\limits_0^T {T^m } e^{ - E/RT} dT , which frequently occurs in the nonisothermal kinetic analysis with the dependence of the frequency factor on the temperature (A=A ₀ T ^m). It is in the following form:

Kinetic analysis of thermal decomposition of some Co-complexes of three unsymmetrical <Emphasis Type="Italic">vic</Emphasis>-dioximes ligands

The thermal decomposition of three new reagent cyclohexylamine-p-tolylglyoxime (L₁H₂), tertiarybutyl amine-p-tolylglyoxime (L₂H₂) and secondary butylamine-p-tolylglyoxime (L₃H₂ and their Co-complexes were studied by both isothermal and nonisothermal methods. As expected, the complex structure of Co-complexes, different steps with different activation energies were realized in decomposition process. Model-fitting and model-free kinetic approaches were applied to nonisothermal and isothermal data. The kinetic triplet (f(α), A and E) related to nonisothermal model-fitting method can not be meaningfully compared with values obtained from isothermal method. The complex nature of the multi-step process of the studied compounds was more easily revealed using a wider temperature range in nonisothermal isoconversional method.     

New linear integral kinetic parameters assessment method based on an accurate approximate formula of temperature integral

This work concerns a proposition of a new assessment method to obtain kinetic parameters from nonisothermal solid-state kinetics, based on a new and accurate approximate formula of temperature integral. The new formula was derived numerically by a two-step linearly fitting process without using any further approximating series. The relative error involved in the activation energy has been estimated and found to be less than 0.001% in the practical range of 15 < x < 60. A comparison of the suggested approximations to published approximates has shown significant improvements in terms of accuracy at high and low x values. The validity of the new method has been confirmed by computing activation energy from experimental data. Moreover, two approaches have been proposed to determine the kinetic reaction model and preexponential factor based on the new approximate formula. The comparison of the obtained results arising from the application of the present method to others obtained by the most widely reported methods in the literature shows a remarkable preeminence of the new method.     

On the evaluation of the nonisothermal kinetic parameters of (GeS2)0.3(Sb2S3)0.7 crystallization using the IKP method

The isoconversional method suggested by Friedman and the invariant kinetic parameters method (IKP) were used in order to examine the kinetics of the nonisothermal crystallization of (GeS₂)_0.3(Sb₂S₃)_0.7. The objective of the paper is to show the usefulness of the IKP method both for determining the activation parameters as well as the model of the investigated process. It was shown that the kinetic triplet [(E, A, f(α), where E is the activation energy, A is the preexponential factor, and f(α) is the differential function of conversion], which results through the application of the IKP method, depends on the set of kinetic models considered. For different sets of kinetic models, proportional values of f(α) are obtained. A criterion for the selection of this set, the use of which lead to the true kinetic triplet corresponding to the analyzed process (E = 163.2 kJ mol^?1; A = 2.47 × 10¹² min^?1 and the Avrami‐Erofeev model, A_m, for m = 2.5–2.6 was suggested. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 309–315, 2004     

Kinetic Analysis of Nonisothermal Decomposition of Acetyl Ferrocene

The work deals with thermal decomposition of acetyl ferrocene in nitrogen atmosphere based on nonisothermal thermogravimetry. It presents a mathematical analysis of nonisothermal thermogravimetric data using multiheating rates to estimate reaction kinetic parameters. Model free (integral isoconversional) methods are employed to analyze the thermogravimetric data. The decomposition is a multistep process. The activation energy E_α of decomposition is conversion (α) dependent. The average values of activation energy are E_α = 49.87, 106.28, and 183.35 kJ mol⁻¹ for three major steps of decomposition. The most probable reaction mechanism function, g(α), for thermal reactions has been identified by the master plot method, and the stepwise reaction mechanisms are found to be different for different steps. The estimated values of the activation energy E_α and g(α) have been utilized in the determination of the reaction rate A_α of thermal decomposition. The α‐dependent reaction rate values are determined and are found to lie in the range of 5.2 × 10⁵ to 3.2 × 10⁴ min⁻¹, 1.7 × 10¹⁵ to 7.8 × 10⁶ min⁻¹, and 3.8 × 10⁸ to 1.4 × 10⁷ min⁻¹ for three different steps. Based on the values of E_α, g(α), and A_α, the thermodynamic triplets (ΔS, ΔH, ΔG) associated with the decomposition reactions have been estimated. Estimated kinetic parameters have been used to construct the conversion curves, and those have been successfully compared with the experimentally observed ones.     

Studies of dehydration kinetics of Li2SO4·H2O by the master plots method

The kinetics of Li₂SO₄·H₂O dehydration in static air atmosphere was studied on the basis of nonisothermal measurements by differential scanning calorimetry. Dehydration data were subjected to an integral composite procedure, which includes an isoconversional method, a master plots method and a model-fitting method. Avrami-Erofeev equation was found to describe all the experimental data in the range of conversion degrees from 0.1 to 0.9. The determined activation energy equals 65.45 kJ·mol⁻¹ with standard deviation ±0.47 kJ·mol⁻¹. The estimated value of parameter m in Avrami-Erofeev equation is 2.15 with standard deviation ±0.11. Also, the obtained pre-exponential factor is 7.79×10⁵ s⁻¹ with standard deviation ±0.55×10⁵ s⁻¹. The results show that the present integral composite procedure gives self-consistent kinetic parameters.     

Synthesis,characterization, and non-isothermal curing kinetics of two silicon-containing arylacetylenic monomers

Vinyltri(phenylethynyl)silane ((ph–C≡C)₃–Si–C=CH₂; VTPES) and phenyltri(phenylethynyl)silane ((ph–C≡C)₃–Si–ph; PTPES) were synthesized by Grignard reaction. Their molecular structures were characterized by means of ¹H NMR, ¹³C NMR, ²⁹Si NMR, and FT-IR spectroscopy. Their nonisothermal thermal curing processes were characterized by DSC, and the corresponding kinetic data, for example activation energy (E), pre-exponential factor (A), and the order of the reaction (n), were obtained by the Kissinger method. The results showed that the melting points of VTPES and PTPES were 84 and 116 °C, respectively. Their curing reaction rates were consistent with first-order kinetic equations. VTPES monomer had a lower activation energy and curing temperature as a result of coordination between reactive groups.     

Kinetic analysis of nonisothermal solid-state reactions: determination of the kinetic parameters by means of a nonlinear regression method

A nonlinear regression method has been proposed for a simultaneous calculation of the activation energy, frequency factor, and reaction order from a single TG curve. This method was based on the new temperature integral approximation proposed in this paper and the Levenberg–Marquardt method. The newly proposed nonlinear regression method was applied for determining the kinetic parameters from two simulated TG curves. The results of the calculations were compared with values obtained by the traditional method. It can be concluded from this comparison that the new nonlinear regression method is more accurate than the traditional method for the determination of the kinetic parameters of solid-state heterogeneous reactions.     

Preparation,Characterization and Non‐isothermal Kinetics of the Dehydration Process of [Sm(p‐MOBA)3bath]2·4H2O

The new complex of [Sm(p‐MOBA)₃bath]₂·4H₂O (p‐MOBA, p‐methoxybenzoate; bath, 4,7‐diphenyl‐1,10‐phenanthroline) was synthesized and characterized by elemental analysis, molar conductance, IR, UV and XRD patterns. The thermal decomposition of the complex was studied under the non‐isothermal condition by TG‐DTG and IR techniques. The most probable mechanism function of the dehydration process was obtained from the analysis of DSC curves of the complex employing the double extrapolated method on the basis of integral isoconversional non‐linear (NL‐INT) and Tang‐Wanjun integral equations. The integral function of the mechanism was [1? (1?α)^1/2]^1/2 and the corresponding kinetic parameters (activation energy E and the pre‐exponential factor A) were obtained.     

An incremental isoconversional method for kinetic analysis based on the orthogonal distance regression

The parameters obtained from a kinetic analysis of thermoanalytical data often exhibit a conversion‐dependent behavior. A novel incremental isoconversional method able to deal with this phenomenon is proposed. The kinetic model is directly fitted to the experimental data using nonlinear orthogonal least squares procedure. The data are processed without transformations, so their error distribution is preserved. As the objective function is based on a maximum likelihood approach, reliable uncertainties of the parameters can be estimated. In contrast to other methods, the activation energy and the pre‐exponential factor are treated as equally important kinetic parameters and are estimated simultaneously. Validity of the method is verified on simulated data, including a dataset with local nonlinearity in the temperature variation. A practical application on the nonisothermal cold crystallization of polyethylene terephthalate is presented. © 2014 Wiley Periodicals, Inc.     

Dependence of the preexponential factor on temperature

Summary The dependence of the preexponential factor on the temperature has been examined and the errors involved in the activation energy calculated from isothermal and non-isothermal methods without considering such dependence have been estimated. It has been shown that the error in the determination of the activation energy calculated ignoring the dependence of Aon Tcan be rather large and it is dependent on x=E/RT, but independent of the experimental method used. It has been also shown that the error introduced by omitting the dependence of the preexponential factor on the temperature is considerably larger than the error due to the Arrhenius integral approach used for carrying out the kinetic analysis of TG data.     

Kinetic studies on the thermal polymerization of N‐chloroacetyl‐11‐aminoundecanoate potassium salt

A potassium salt of N‐chloroacetyl‐11‐aminoundecanoate was thermally polymerized to obtain the corresponding poly(glycolic acid‐alt‐11‐aminoundecanoic acid). A kinetic study was then performed that was based on isothermal and nonisothermal polymerizations performed in a differential scanning calorimeter. The complete kinetic triplet was determined (the activation energy, pre‐exponential factor, and integral function of the degree of conversion). A kinetic analysis was performed with an integral isoconversional procedure (free model), and the kinetic model was determined both with the Coats–Redfern method (the obtained isoconversional value being accepted as the effective activation energy) and through the compensation effect. The polymerization followed a three‐dimensional growth‐of‐nuclei (Avrami) kinetic mechanism. Isothermal polymerization was simulated with nonisothermal data. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1166–1176, 2005     

New incremental isoconversional method for kinetic analysis of solid thermal decomposition

A simple and precise incremental isoconversional integral method based on Li-Tang (LT) method is proposed for kinetic analysis of solid thermal decomposition, in order to evaluate the activation energy as a function of conversion degree. The new method overcomes the limitation of LT method in which the calculated activation energy is influenced by the lower limit of integration. By applying the new method to kinetic analysis of both the simulated nonisothermal case and experimental case of strontium carbonate thermal decomposition, it is shown that the dependence of activation energy on conversion degree evaluated by the new method is consistent with those obtained by Friedman (FR) method and the modified Vyazovkin method. As the new method is free from approximating the temperature integral and not sensitive to the noise of the kinetic data, it is believed to be more convenient in nonisothermal kinetic analysis of solid decompositions.     

Precision of integral methods for the determination of the kinetic parameters

In this paper, a systematic analysis of the errors involved in the determination of the kinetic parameters (including the activation energy and frequency factor) from five integral methods has been carried out. The integral methods analyzed here are Coats-Redfern, Gorbachev, Wanjun-Yuwen-Hen-Zhiyong-Cunxin, Junmeng-Fusheng-Weiming-Fang, Junmeng-Fang and Junmeng-Fang-Weiming-Fusheng method. The results have shown that the precision of the kinetic parameters calculated by the different integral methods is dependent on u (E/RT), that is, on the activation energy and the average temperature of the process.     

Error evaluation of integral methods by consideration on the approximation of temperature integral

Summary In this paper, the integral methods in general use are divided into two types in terms of their different ways to in order to deal with the temperature integral p(x): for Type A the function h(x)=p(x)x²e^x is regarded as constant vs. x, while for Type B h(x) varies vs. x and ln[p(x)] is assumed to have the approximation form of ln[p(x)]=alnx+bx+c (the coefficients a, b, and c are constant). The errors of kinetic parameters calculated by these two types of methods are derived as functions of x and analyzed theoretically. It is found that Type A methods have the common errors of activation energy, while the Coats-Redfern method can lead to more accurate value of frequency factor than others. The accuracy of frequency factor can be further enhanced by adjusting the expression of the Coats-Redfern approximation. Although using quite simple approximation of the temperature integral, the Coats-Redfern method has the best performance among Type A methods, implying that usage of a sophisticated approximation may be unnecessary in kinetic analysis. For Type B, the revised MKN method has a lower error in activation energy and an acceptable error in frequency factor, and thus it can be reliably used. Comparatively, the Doyle method has higher error of activation energy and great error of the frequency factor, and thus it is not recommended to be adopted in kinetic analysis.